# Is #f(x)=sqrt(ln(x)^2)# increasing or decreasing at #x=1#?

##### 1 Answer

x = 1 meets the two branches of log graphs representng this equation, at the common point (1. 0). This is a node for the graph. f(x) is increasing for one branch and decreasing for the other.

#### Explanation:

Importantly, the statement

.So, the given equation is the combined equation for the pair

y = f(x) = + ln x and y =

For x > 1, the graph for the first is above the x-axis It is below the x-axis, for 0 < x < 1,

For the graph of the second equation in the pair, it is vice versa.

y-axis ( x = 0 ) is the asymptote.

Separately, f'(x) =

Anyway, at x = 1, y = 0 and f'(1) = +1 > 0 for one branch, and